It is crucial for the existence of an intrinsically-defined holographic dual theory that scattering amplitudes not only exhibit a global conformal symmetry, but also admit other behavior characteristic of a two-dimensional theory. The Ward identities for infinite-dimensional symmetries that follow from soft theorems are powerful and encouraging examples of this behavior. In particular, the subleading soft graviton theorem implies that the global conformal symmetry is enhanced to a local Virasoro symmetry generated by a stress tensor [1]}, [2]}, [3]}, [4]}. Similarly, the leading soft theorem in gauge theory implies a local Kac-Moody symmetry generated by a Kac-Moody current [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Finally, soft theorems at other orders in gauge and gravitational theories give rise to additional infinite-dimensional symmetries generated by generalized 2D currents [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}. This collection of currents was recently shown to admit a rich symmetry algebra [23]}, which has been identified as a \({\rm w}_{1 +\infty }\)  algebra [29]}.
